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A note on the exact closed form solution for coupled Hill equations
Author(s) -
Watanabe Kazumi
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000200
Subject(s) - cartesian coordinate system , orthotropic material , exact solutions in general relativity , displacement (psychology) , mathematics , mathematical analysis , coordinate system , closed form expression , simultaneous equations , polar coordinate system , geometry , physics , differential equation , thermodynamics , finite element method , psychology , psychotherapist
An exact closed form solution for coupled (simultaneous) Hill equations is found. The Hill equations are derived from the displacement equations for the 2D orthotropic elastic solid by introducing polar coordinate variables to the Cartesian components of the displacement, and a solution method for a little bit generalized form of the Hill equations is presented.